Spatially varying cross-correlation coefficients in the presence of nugget effects

• 成果类型: Article
• 署名作者: Kleiber, William; Genton, Marc G.
• 署名单位: University of Colorado System; University of Colorado Boulder; King Abdullah University of Science & Technology
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ass057
• 发表日期: 2013
• 页码: 213220
• 关键词: multivariate random-fields; covariance functions; MODEL

摘要

We derive sufficient conditions for the cross-correlation coefficient of a multivariate spatial process to vary with location when the spatial model is augmented with nugget effects. The derived class is valid for any choice of covariance functions, and yields substantial flexibility between multiple processes. The key is to identify the cross-correlation coefficient matrix with a contraction matrix, which can be either diagonal, implying a parsimonious formulation, or a fully general contraction matrix, yielding greater flexibility but added model complexity. We illustrate the approach with a bivariate minimum and maximum temperature dataset in Colorado, allowing the two variables to be positively correlated at low elevations and nearly independent at high elevations, while still yielding a positive definite covariance matrix.